TY - JOUR
T1 - Separation of variables and exact solutions to nonlinear diffusion equations with x-dependent convection and absorption
AU - Jia, Huabing
AU - Xu, Wei
AU - Zhao, Xiaoshan
AU - Li, Zhanguo
PY - 2008/3/15
Y1 - 2008/3/15
N2 - This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D (u) ux)x + Q (x, u) ux + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.
AB - This paper considers nonlinear diffusion equations with x-dependent convection and source terms: ut = (D (u) ux)x + Q (x, u) ux + P (x, u). The functional separation of variables of the equations is studied by using the generalized conditional symmetry approach. We formulate conditions for such equations which admit the functionally separable solutions. As a consequence, some exact solutions to the resulting equations are constructed. Finally, we consider a special case for the equations which admit the functionally separable solutions when the convection and source terms are independent of x.
KW - Exact solutions
KW - Generalized conditional symmetry
KW - Nonlinear diffusion equations
KW - Separation of variables
UR - https://www.scopus.com/pages/publications/35348960427
U2 - 10.1016/j.jmaa.2007.07.063
DO - 10.1016/j.jmaa.2007.07.063
M3 - 文章
AN - SCOPUS:35348960427
SN - 0022-247X
VL - 339
SP - 982
EP - 995
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -